More relaxed non-quadratic stabilization conditions for TS fuzzy control systems using LMI and GEVP

Vafamand, Navid; Sadeghi, Mehdi

doi:10.1007/s12555-013-0497-7

Cited by 24 publications

(20 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Though they lead to BMI conditions in Theorem 1. In the following, a novel iterative method is proposed to find feasible solutions of constraints (15) and (16) in Theorem 1.…”

Section: Discussion About Conservativenessmentioning

confidence: 99%

Bilinear matrix inequality‐based nonquadratic controller design for polytopic‐linear parameter varying systems

Javanmardi

Dehghani

Mohammadi

et al. 2020

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

This article proposes relaxed sufficient bilinear matrix inequality (BMI) conditions to design a gain-scheduling controller for nonlinear systems described by polytopic-linear parameter varying (LPV) representations. The obtained conditions are derived based on a nonquadratic Lyapunov function and a parallel distributed compensator scheme. The controller design procedure involves some novel null terms and leads to a BMI problem, which hardly has been solved in previous researches. Furthermore, to effectively solve the BMI conditions, a novel sequential approach is proposed which convert the overall BMI problem into linear matrix inequality (LMI) constraints and some simpler BMI conditions with fewer dimensions than the original one. Initially, the LMI conditions are solved as a convex optimization problem. Second, the BMI terms are iteratively linearized near the feasible solutions of the LMIs and each solution candidates for the BMI constraints. Finally, the linearized condition is solved as an eigenvalue problem. To show the merits of the proposed approach, several numerical comparisons and simulations are provided.

show abstract

“…Though they lead to BMI conditions in Theorem 1. In the following, a novel iterative method is proposed to find feasible solutions of constraints (15) and (16) in Theorem 1.…”

Section: Discussion About Conservativenessmentioning

confidence: 99%

Bilinear matrix inequality‐based nonquadratic controller design for polytopic‐linear parameter varying systems

Javanmardi

Dehghani

Mohammadi

et al. 2020

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

show abstract

“…In this section, we will present some fruitful slack matrices and lemmas that will be used in the proof procedure of the main results. Based on the convex sum property of membership functions (3), the following null term is defined [34]:…”

Section: Slack Matrices and Fruitful Lemmasmentioning

confidence: 99%

TS Fuzzy Model-Based Controller Design for a Class of Nonlinear Systems Including Nonsmooth Functions

Vafamand

Asemani

Khayatiyan

et al. 2020

IEEE Trans. Syst. Man Cybern, Syst.

Self Cite

View full text Add to dashboard Cite

This paper proposes a novel robust controller design for a class of nonlinear systems including hard nonlinearity functions. The proposed approach is based on Takagi-Sugeno (TS) fuzzy modeling, nonquadratic Lyapunov function, and nonparallel distributed compensation scheme. In this paper, a novel TS modeling of the nonlinear dynamics with signum functions is proposed. This model can exactly represent the original nonlinear system with hard nonlinearity while the discontinuous signum functions are not approximated. Based on the bounded-inputbounded-output stability scheme and L 1 performance criterion, new robust controller design conditions in terms of linear matrix inequalities are derived. Three practical case studies, electric power steering system, a helicopter model and servo-mechanical system, are presented to demonstrate the importance of such class of nonlinear systems comprising signum function. Furthermore, to show the superiorities of the proposed approach, it is applied to these systems; and, the experimental real-time hardware-inthe-loop results are compared with the published literature with the same topic. Index Terms-Electric power steering (EPS) system, hardwarein-the-loop (HIL), helicopter system, nonsmooth dynamical equations, robust L 1 controller, servo-system, signum function, Takagi-Sugeno (TS) fuzzy model.

show abstract

“…In this paper, a simple but effective linear state feedback controller is proposed for injecting a stabilizing power to the DC MGs with multiple CPLs. This approach employs the LMI technique to numerically compute controller gain matrix [26]- [28]. In other words, for a DC MG with the given system parameters, the state-space matrices , , and are known.…”

Section: Remark 4 (Design Procedures Of the Proposed Controller)mentioning

confidence: 99%

“…According to the assumptions of (33) in Section III, the nonlinear-linear system (9) and (26) satisfy the following equation…”

Section: Remark 4 (Design Procedures Of the Proposed Controller)mentioning

confidence: 99%

Improved Stabilization of Nonlinear DC Microgrids: Cubature Kalman Filter Approach

Kardan

Asemani

Khayatian

et al. 2018

IEEE Trans. on Ind. Applicat.

Self Cite

View full text Add to dashboard Cite

This paper investigates the injecting power stabilization of nonlinear DC microgrids (MGs) with constant power loads (CPLs). By considering a centralized controller scheme, the limitations of the communication utilities are considered. Therefore, limited information is transferred through the non-ideal noisy communication network. Consequently, a cubature Kalman filter (CKF) with a 3rd degree is proposed to mitigate the effect of the noisy measurement and the noisy network on the system's information. Moreover, an estimationbased robust feedback controller is developed to design an optimal value for the injecting power. The considered CKF algorithm is robust against the system uncertainty and noisy environments and has a low computational time for high-order DC MGs with a high number of sources and CPLs. In addition, a systematic procedure to compute the feedback gain of the controller is presented which can numerically be solved by linear matrix inequality (LMI) techniques. Hardware-in-the-loop (HiL) real-time simulation results verify the simplicity of the controller implementation, enhanced performance for the case of limited information, and better robustness against the noisy measurements compared to the state-of-the-art methods. Index Terms-DC microgrid, constant power load, Cubature Kalman filter (CKF), linear matrix inequality (LMI), non-ideal communication network, hardware-in-the-loop (HiL).

show abstract

More relaxed non-quadratic stabilization conditions for TS fuzzy control systems using LMI and GEVP

Cited by 24 publications

References 17 publications

Bilinear matrix inequality‐based nonquadratic controller design for polytopic‐linear parameter varying systems

Bilinear matrix inequality‐based nonquadratic controller design for polytopic‐linear parameter varying systems

TS Fuzzy Model-Based Controller Design for a Class of Nonlinear Systems Including Nonsmooth Functions

Improved Stabilization of Nonlinear DC Microgrids: Cubature Kalman Filter Approach

Contact Info

Product

Resources

About